Coloured noise influence on system evolution

Within the power-law approach for noise amplitude dependence on stochastic variables, we present a picture of noise-induced transitions in systems affected by coloured multiplicative noise. The governed equations for main statistical moments are obtained and investigated in detail. We show that a reentrant noise-induced transition is realized within a window of the control parameter. Received 15 October 2001 / Received in final form 8 July 2002 Published online 17 September 2002     

The impact factor for the virtual photonto light vector meson transition

We evaluate in the next-to-leading approximation the forward impact factor for the virtual photon to light vector meson transition in the case of longitudinal polarization. We find that in the hard kinematic domain, both in the leading and in the next-to-leading approximation, the expression for the impact factor factorizes, up to power suppressed corrections, into the convolution of a perturbatively calculable hard-scattering amplitude and a meson twist-2 distribution amplitude.Received: 20 May 2004, Revised: 28 September 2004, Published online: 15 November 2004     

Two-photon annihilation into baryon-antibaryon pairs

We study the handbag contribution to two-photon annihilation into baryon-antibaryon pairs at large energy and momentum transfer. We derive factorization of the process amplitude into a hard subprocess and form factors describing the soft transition, assuming that the process is dominated by configurations where the (anti)quark approximately carries the full momentum of the (anti)baryon. The form factors represent moments of time-like generalized parton distributions, so-called distribution amplitudes. A characteristic feature of the handbag mechanism is the absence of isospin-two components in the final state, which in combination with flavor symmetry provides relations among the form factors for the members of the lowest-lying baryon octet. Assuming dominance of the handbag contribution, we can describe current experimental data with form factors of plausible size, and predict the cross sections of presently unmeasured channels. Received: 3 July 2002 / Revised version: 7 October 2002 / Published online: 20 November 2002 RID="a" ID="a" e-mail: mdiehl@physik.rwth-aachen.de RID="b" ID="b" e-mail: kroll@physik.uni-wuppertal.de RID="c" ID="c" e-mail: cvogt@nordita.dk     

Charmless hadronic decays of B mesons to a pseudoscalar and a tensor meson

We study two-body charmless hadronic decays of B mesons to a pseudoscalar meson (P) and a tensor meson (T) in the frameworks of both flavor SU(3) symmetry and generalized factorization. Certain ways to test the validity of the generalized factorization are proposed, based on the flavor SU(3) analysis. We present a set of relations between a flavor SU(3) amplitude and the corresponding amplitude in the generalized factorization which bridge both approaches in decays. The branching ratios and CP asymmetries are calculated using the full effective Hamiltonian including all the penguin operators and the form factors obtained in the non-relativistic quark model of Isgur, Scora, Grinstein and Wise. We identify the decay modes in which the branching ratios and CP asymmetries are expected to be relatively large. Received: 6 July 2001 / Revised version: 8 October 2001 / Published online: 30 November 2001     

Twist-4 photon helicity-flip amplitude in DVCS on a nucleon in the Wandzura-Wilczek approximation

We computed the twist-4 part of the photon spin-flip amplitude in deeply virtual Compton scattering on a nucleon in the Wandzura–Wilczek approximation. We found a factorizable contribution, which arises from photon scattering on quarks with non-zero angular momentum along the collision axis. As the genuine twist-2 amplitude arises at the NLO, for moderate virtualities of the hard photon, GeV, a kinematical twist-4 correction can give a numerically important contribution to the photon helicity-flip amplitude. Received: 2 July 2001 / Revised version: 17 July 2001 / Published online: 31 August 2001     

Charge and transition form factors of light mesons in LFQM

The charge and transition form factors of pions (, , and ) are studied in the light-front quark model (LFQM). We find that our results for and agree well with experiment. Furthermore, the mixing of and is considered. We also calculate and and compare them with the data. Received: 23 November 2000 / Revised version: 23 December 2000 / Published online: 23 February 2001     

Solute effects on the helix-coil transition

We discuss the effects of the solvent composition on the helix-coil transition of a polypeptide chain. We use a simple model to demonstrate that improving the hydrogen-bonding ability of the solvent can make the transition less cooperative, without affecting the transition temperature. This effect is very different from other solvent effects which primarily influence the melting transition rather than the cooperativity. Received 10 December 2001 and Received in final form 22 March 2002     

Timelike Compton scattering: exclusive photoproduction of lepton pairs

We investigate the exclusive photoproduction of a heavy timelike photon which decays into a lepton pair, . This can be seen as the analog of deeply virtual Compton scattering, and we argue that the two processes are complementary for studying generalized parton distributions in the nucleon. In an unpolarized experiment the angular distribution of the leptons readily provides access to the real part of the Compton amplitude. We estimate the possible size of this effect in kinematics where the Compton process should be dominated by quark exchange. Received: 9 October 2001 / Published online: 5 April 2002     

Resonance estimates of \mathcal{O}(p^6) low-energy constants and QCD short-distance constraints

Starting from the study of the low-energy and high-energy behaviors of the QCD three-point functions , and , several low-energy constants of the chiral Lagrangian are evaluated within the framework of the lowest meson dominance (LMD) approximation to the large- limit of QCD. In certain cases, values that differ substantially from estimates based on a resonance Lagrangian are obtained. It is pointed out that the differences arise through the fact that QCD short-distance constraints are in general not correctly taken into account in the approaches using resonance Lagrangians. We discuss the implications of our results for the counterterm contributions to the vector form factor of the pion and to the decay , and for the pion–photon–photon transition form factor. Received: 4 June 2001 / Published online: 31 August 2001     

Behavior of the hadron potential at large distances and properties of the hadron spin-flip amplitude

The impact of the form of the hadron potential at large distances on the behavior of the hadron spin-flip amplitude at small angles is examined. The t-dependence of the spin-flip amplitude of high-energy hadron elastic scattering is analyzed under different assumptions on the hadron interaction. It is shown that the long tail of the nonGaussian form of the hadron potential of the hadron interaction in the impact parameter representation leads to a large value of the slope of the spin-flip amplitude (without the kinematical factor ) as compared with the slope of the spin-nonflip amplitude. This effect can explain the form of the differential cross-section and the analyzing power at small transfer momenta. The methods for the definition of the spin-dependent part of the hadron scattering amplitude are presented. A possibility to investigate the structure of the hadron spin-flip amplitude from the accurate measure of the differential cross-section and the spin correlation parameters is shown. Received: 14 December 2001 / Accepted: 17 January 2002     

Analytic coupling and Sudakov effects in exclusive processes: pion and \gamma ^*\gamma \to \pi ^0 form factors

We develop and discuss in technical detail an infrared-finite factorization and optimized renormalization scheme for calculating exclusive processes, which enables the inclusion of transverse degrees of freedom without entailing suppression of calculated observables, like form factors. This is achieved by employing an analytic, i.e., infrared stable, running strong-coupling which removes the Landau singularity at by a minimum power-behaved correction. The ensuing contributions to the cusp anomalous dimension – related to the Sudakov form factor – and to the quark anomalous dimension – which controls evolution – lead to an enhancement at high of the hard part of exclusive amplitudes, calculated in perturbative QCD, while simultaneously improving its scaling behavior. The phenomenological implications of this framework are analyzed by applying it to the pion's electromagnetic form factor, including the NLO contribution to the hard-scattering amplitude, and also to the pion–photon transition at LO. For the pion wave function, an improved ansatz of the Brodsky–Huang–Lepage type is employed, which includes an effective (constituent-like) quark mass, GeV. Predictions for both form factors are presented and compared to the experimental data, applying Brodsky–Lepage–Mackenzie commensurate scale setting. We find that the perturbative hard part prevails at momentum transfers above about 20 GeV, while at lower values the pion form factor is dominated by Feynman-type contributions. The theoretical prediction for the form factor indicates that the true pion distribution amplitude may be somewhat broader than the asymptotic one. Received: 19 May 2000 / Revised version: 16 August 2000 / Published online: 13 November 2000     

The form factors in (HI,HI') direct reactions

Using a semiclassical theory, we analyze the inelastic transition form factor. We find that: (i) In the strong absorption limit, the Austern-Blair theory is a good approximation to the inelastic form factor — even in highly mismatched reactions, (ii) In weak to moderate absorption, the amplitude of the inelastic form factor oscillates due to overlapping potential resonances. Here the internal part of the form factor can be expressed in a simple form, which may easily be used to analyze heavy-ion inelastic scattering, (iii) In the presence of an isolated resonance, the inelastic form factor is enhanced greatly at the resonance due to multiple reflections inside the potential well.     

Core percolation in random graphs: a critical phenomena analysis

We study both numerically and analytically what happens to a random graph of average connectivity α when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated vertices plus an induced subgraph we call the core. In the thermodynamic limit of an infinite random graph, we compute analytically the dynamics of leaf removal, the number of isolated vertices and the number of vertices and edges in the core. We show that a second order phase transition occurs at α = e = 2.718 ... : below the transition, the core is small but above the transition, it occupies a finite fraction of the initial graph. The finite size scaling properties are then studied numerically in detail in the critical region, and we propose a consistent set of critical exponents, which does not coincide with the set of standard percolation exponents for this model. We clarify several aspects in combinatorial optimization and spectral properties of the adjacency matrix of random graphs. Received 31 January 2001 and Received in final form 26 June 2001     

New amplitude equation of single—mode laser

The white-gain model and the white-loss model of a single-mode laser are investigated in the presence of cross-correlations between the real and imaginary parts of quantum noise as well as pump noise. It was found that, like the white cubic model (2001 Chin. Phys. Lett. 18 370), the amplitude equations are all decoupled from the phase equations for the two models, and the same novel term appears in the amplitude equations of the two models. So we can put the amplitude equations of all the models into a general form, that is, the new amplitude equation. We further use this new amplitude equation to study specifically the stationary properties of the laser intensity for the white-gain model.     

Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media

We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.     

The transition from two-dimensional to three-dimensional foam structures

Small cells in an experimental sample of two-dimensional foam, such as that which is contained between two glass plates, may undergo a transition to a three-dimensional form, becoming detached from one boundary. We present the first detailed observations of this phenomenon, together with computer simulations. The transition is attributed to an instability of the Rayleigh-Plateau type. A theoretical analysis is given which shows that an individual cell is susceptible to this instability only if it has less than six sides. Received 15 October 2001 and Received in final form 14 January 2002     

Melting and unzipping of DNA

Existing experimental studies of the thermal denaturation of DNA yield sharp steps in the melting curve suggesting that the melting transition is first order. This transition has been theoretically studied since the early sixties, mostly within an approach in which the microscopic configurations of a DNA molecule consist of an alternating sequence of non-interacting bound segments and denaturated loops. Studies of these models neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. In the present study we take into account in an approximate way the excluded-volume interaction between denaturated loops and the rest of the chain. This is done by exploiting recent results on scaling properties of polymer networks of arbitrary topology. We also ignore the heterogeneity of the polymer. We obtain a first-order melting transition in d = 2 dimensions and above, consistent with the experimental results. We also consider within our approach the unzipping transition, which takes place when the two DNA strands are pulled apart by an external force acting on one end. We find that the under equilibrium condition the unzipping transition is also first order. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. For instance, the loop size distribution decays algebraically at the transition and the length of the denaturated end segment diverges as the transition is approached. We evaluate these critical properties within our approach. Received 21 August 2001 and Received in final form 26 January 2002     

Baryon form factors in chiral perturbation theory

We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the charge radius and the – transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory. Received: 25 October 2000 / Published online: 23 January 2001     

Coherent control of the self-trapping transition

We discuss the dynamics of two weakly coupled Bose-Einstein condensates in a double-well potential, contrasting the mean-field picture to the exact N-particle evolution. On the mean-field level, a self-trapping transition occurs when the scaled interaction strength exceeds a critical value; this transition essentially persists in small condensates comprising about 1000 atoms. When the double-well is modulated periodically in time, Floquet-type solutions to the nonlinear Schr?dinger equation take over the role of the stationary mean-field states. These nonlinear Floquet states can be classified as “unbalanced” or “balanced”, depending on whether or not they entail long-time confinement of most particles to one well. Since the emergence of unbalanced Floquet states depends on the amplitude and frequency of the modulating force, we predict that the onset of self-trapping can efficiently be controlled by varying these parameters. This prediction is verified numerically by both mean-field and N-particle calculations. Received 5 November 2000 and Received in final form 16 February 2001